Question

if $sin10A^{\circ }=cos(2A-30{)}^{\circ }$, then the value of A in degrees is ____ .

• A. $A={10}^{\circ }$
• B. $A={20}^{\circ }$
• C. $A={30}^{\circ }$
• D. $A={40}^{\circ }$

Answer 1

The correct option is A $A={10}^{\circ }$

$sin10A^{\circ }=cos(2A-30{)}^{\circ }$

$\because$ $cos({90}^{\circ }-\theta )$ = $sin\left(\theta \right)$

On rearranging the equation with one trigonometric ratio on each side, we get​

$\Rightarrow cos({90}^{\circ }-10A)=cos(2A-30{)}^{\circ }$

$\Rightarrow {90}^{\circ }-10A=2A-{30}^{\circ }$

$\Rightarrow 12A={120}^{\circ }$

$\Rightarrow A={10}^{\circ }$